{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Untitled16.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "LNx5NEOMscgf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "40dfe21d-b743-44cd-c959-9267c0265a84"
      },
      "source": [
        "import numpy as np\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "input_data = np.array([math.cos(x) for x in np.arange(200)])\n",
        "plt.plot(input_data[:50])\n",
        "plt.show"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<function matplotlib.pyplot.show>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 1
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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sOuZZaKjTZbhgziEY5kZqKlOdLH4XgM8yxgbjHfsZY0cB/CiADxHRLaPeyBh7lDF2lDF2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\nCYKIiOISBBERxX0CxMSyI3dPECAAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qH2y3a35tXpt",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = []\n",
        "Y = []\n",
        "\n",
        "size = 50\n",
        "number_of_records = len(input_data) - size\n",
        "for i in range(number_of_records - 50):\n",
        "  X.append(input_data[i:i+size])\n",
        "  Y.append(input_data[i+size])\n",
        "X = np.array(X)\n",
        "X = np.expand_dims(X, axis=2)\n",
        "Y = np.array(Y)\n",
        "Y = np.expand_dims(Y, axis=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C4twJdIstiet",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "aadd6289-1973-4256-e3c5-347df26faccb"
      },
      "source": [
        "X.shape, Y.shape"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((100, 50, 1), (100, 1))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tlHSvArxtmxx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X_valid = []\n",
        "Y_valid = []\n",
        "for i in range(number_of_records - 50, number_of_records):\n",
        "    X_valid.append(input_data[i:i+size])\n",
        "    Y_valid.append(input_data[i+size])\n",
        "X_valid = np.array(X_valid)\n",
        "X_valid = np.expand_dims(X_valid, axis=2)\n",
        "Y_valid = np.array(Y_valid)\n",
        "Y_valid = np.expand_dims(Y_valid, axis=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YcXY7xNPtrrp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "learning_rate = 0.0001\n",
        "number_of_epochs = 5\n",
        "sequence_length = 50\n",
        "hidden_layer_size = 100\n",
        "output_layer_size = 1\n",
        "back_prop_truncate = 5\n",
        "min_clip_value = -10\n",
        "max_clip_value = 10"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VA4qjj07tuj4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "W1 = np.random.uniform(0, 1, (hidden_layer_size, sequence_length))\n",
        "W2 = np.random.uniform(0, 1, (hidden_layer_size, hidden_layer_size))\n",
        "W3 = np.random.uniform(0, 1, (output_layer_size, hidden_layer_size))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Njl-MZA0tw-4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sigmoid(x):\n",
        "    return 1 / (1 + np.exp(-x))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FFiHWEO8uH6w",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "6e46817c-fcb4-4e82-95ab-d69e11a02999"
      },
      "source": [
        "for epoch in range(number_of_epochs):\n",
        "  # check loss on train\n",
        "  loss = 0.0\n",
        "  \n",
        "  # do a forward pass to get prediction\n",
        "  for i in range(Y.shape[0]):\n",
        "    x, y = X[i], Y[i]\n",
        "    prev_act = np.zeros((hidden_layer_size, 1))\n",
        "    for t in range(sequence_length):\n",
        "      new_input = np.zeros(x.shape)\n",
        "      new_input[t] = x[t]\n",
        "      mul_w1 = np.dot(W1, new_input)\n",
        "      mul_w2 = np.dot(W2, prev_act)\n",
        "      add = mul_w2 + mul_w1\n",
        "      act = sigmoid(add)\n",
        "      mul_w3 = np.dot(W3, act)\n",
        "      prev_act = act\n",
        "\n",
        "  # calculate error \n",
        "    loss_per_record = (y - mul_w3)**2 / 2\n",
        "    loss += loss_per_record\n",
        "  loss = loss / float(y.shape[0])\n",
        "  \n",
        "  # check loss on validation\n",
        "  val_loss = 0.0\n",
        "  for i in range(Y_valid.shape[0]):\n",
        "    x, y = X_valid[i], Y_valid[i]\n",
        "    prev_act = np.zeros((hidden_layer_size, 1))\n",
        "    for t in range(sequence_length):\n",
        "      new_input = np.zeros(x.shape)\n",
        "      new_input[t] = x[t]\n",
        "      mul_w1 = np.dot(W1, new_input)\n",
        "      mul_w2 = np.dot(W2, prev_act)\n",
        "      add = mul_w2 + mul_w1\n",
        "      act = sigmoid(add)\n",
        "      mul_w3 = np.dot(W3, act)\n",
        "      prev_act = act\n",
        "\n",
        "    loss_per_record = (y - mul_w3)**2 / 2\n",
        "    val_loss += loss_per_record\n",
        "  val_loss = val_loss / float(y.shape[0])\n",
        "\n",
        "  print('Epoch: ', epoch + 1, ', Loss: ', loss, ', Val Loss: ', val_loss)\n",
        "  \n",
        "  # train model\n",
        "  for i in range(Y.shape[0]):\n",
        "    x, y = X[i], Y[i]\n",
        "  \n",
        "    layers = []\n",
        "    prev_act = np.zeros((hidden_layer_size, 1))\n",
        "    dW1 = np.zeros(W1.shape)\n",
        "    dW3 = np.zeros(W3.shape)\n",
        "    dW2 = np.zeros(W2.shape)\n",
        "    \n",
        "    dW1_t = np.zeros(W1.shape)\n",
        "    dW3_t = np.zeros(W3.shape)\n",
        "    dW2_t = np.zeros(W2.shape)\n",
        "    \n",
        "    dW1_i = np.zeros(W1.shape)\n",
        "    dW2_i = np.zeros(W2.shape)\n",
        "    \n",
        "    # forward pass\n",
        "    for t in range(sequence_length):\n",
        "      new_input = np.zeros(x.shape)\n",
        "      new_input[t] = x[t]\n",
        "      mul_w1 = np.dot(W1, new_input)\n",
        "      mul_w2 = np.dot(W2, prev_act)\n",
        "      add = mul_w2 + mul_w1\n",
        "      act = sigmoid(add)\n",
        "      mul_w3 = np.dot(W3, act)\n",
        "      layers.append({'act':act, 'prev_act':prev_act})\n",
        "      prev_act = act\n",
        "\n",
        "    # derivative of pred\n",
        "    dmul_w3 = (mul_w3 - y)\n",
        "    \n",
        "    # backward pass\n",
        "    for t in range(sequence_length):\n",
        "      dW3_t = np.dot(dmul_w3, np.transpose(layers[t]['act']))\n",
        "      dsv = np.dot(np.transpose(W3), dmul_w3)\n",
        "      \n",
        "      ds = dsv\n",
        "      dadd = add * (1 - add) * ds\n",
        "      \n",
        "      dmul_w2 = dadd * np.ones_like(mul_w2)\n",
        "\n",
        "      dprev_act = np.dot(np.transpose(W2), dmul_w2)\n",
        "\n",
        "\n",
        "      for i in range(t-1, max(-1, t-back_prop_truncate-1), -1):\n",
        "        ds = dsv + dprev_act\n",
        "        dadd = add * (1 - add) * ds\n",
        "\n",
        "        dmul_w2 = dadd * np.ones_like(mul_w2)\n",
        "        dmul_w1 = dadd * np.ones_like(mul_w1)\n",
        "\n",
        "        dW2_i = np.dot(W2, layers[t]['prev_act'])\n",
        "        dprev_act = np.dot(np.transpose(W2), dmul_w2)\n",
        "\n",
        "        new_input = np.zeros(x.shape)\n",
        "        new_input[t] = x[t]\n",
        "        dW1_i = np.dot(W1, new_input)\n",
        "        dx = np.dot(np.transpose(W1), dmul_w1)\n",
        "\n",
        "        dW1_t += dW1_i\n",
        "        dW2_t += dW2_i\n",
        "        \n",
        "      dW3 += dW3_t\n",
        "      dW1 += dW1_t\n",
        "      dW2 += dW2_t\n",
        "      \n",
        "      if dW1.max() > max_clip_value:\n",
        "        dW1[dW1 > max_clip_value] = max_clip_value\n",
        "      if dW3.max() > max_clip_value:\n",
        "        dW3[dW3 > max_clip_value] = max_clip_value\n",
        "      if dW2.max() > max_clip_value:\n",
        "        dW2[dW2 > max_clip_value] = max_clip_value\n",
        "        \n",
        "      \n",
        "      if dW1.min() < min_clip_value:\n",
        "        dW1[dW1 < min_clip_value] = min_clip_value\n",
        "      if dW3.min() < min_clip_value:\n",
        "        dW3[dW3 < min_clip_value] = min_clip_value\n",
        "      if dW2.min() < min_clip_value:\n",
        "        dW2[dW2 < min_clip_value] = min_clip_value\n",
        "    \n",
        "    # update\n",
        "    W1 -= learning_rate * dW1\n",
        "    W3 -= learning_rate * dW3\n",
        "    W2 -= learning_rate * dW2"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch:  1 , Loss:  [[129321.80142656]] , Val Loss:  [[64655.76954217]]\n",
            "Epoch:  2 , Loss:  [[83469.71575242]] , Val Loss:  [[41730.74354188]]\n",
            "Epoch:  3 , Loss:  [[47617.6300782]] , Val Loss:  [[23805.71754155]]\n",
            "Epoch:  4 , Loss:  [[21765.54373458]] , Val Loss:  [[10880.69120694]]\n",
            "Epoch:  5 , Loss:  [[5911.30616237]] , Val Loss:  [[2954.59044314]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SDoEVpWdvXc0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 267
        },
        "outputId": "0c54c124-6318-4494-e93c-41ffe70dc666"
      },
      "source": [
        "preds = []\n",
        "for i in range(Y_valid.shape[0]):\n",
        "  x, y = X_valid[i], Y_valid[i]\n",
        "  prev_act = np.zeros((hidden_layer_size, 1))\n",
        "  # For each time step...\n",
        "  for t in range(sequence_length):\n",
        "    mul_w1 = np.dot(W1, x)\n",
        "    mul_w2 = np.dot(W2, prev_act)\n",
        "    add = mul_w2 + mul_w1\n",
        "    act = sigmoid(add)\n",
        "    mul_w3 = np.dot(W3, act)\n",
        "    prev_act = act\n",
        "\n",
        "  preds.append(mul_w3)\n",
        "  \n",
        "preds = np.array(preds)\n",
        "\n",
        "plt.plot(preds[:, 0, 0], 'g')\n",
        "plt.plot(Y_valid[:, 0], 'r')\n",
        "plt.show()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dc8oFhmbCn5lhOQadcfzlpD4Pfu3jqu+5kWxSxZzwR0db3zQ2xlabSfXGZvzv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\nr9FoNCnC/wOU/9itrT1KJAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ceF8T8M0vhNi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "f1f59499-3165-4679-bc49-b60d6055ea33"
      },
      "source": [
        "from sklearn.metrics import mean_squared_error\n",
        "math.sqrt(mean_squared_error(Y_valid[:, 0], preds[:, 0, 0]))"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.440276702954115"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    }
  ]
}